Reliability-based design optimization using convex linearization and sequential optimization and reliability assessment method

In this study, an effective method for reliability-based design optimization (RBDO) is proposed enhancing sequential optimization and reliability assessment (SORA) method by convex linearization. In SORA, reliability estimation and deterministic optimization are performed sequentially. And the sensitivity and function value of probabilistic constraint at the most probable point (MPP) are obtained in the process of finding reliability information. In this study, the convex linearization is constructed by utilizing the sensitivity and function value of the probabilistic constraint at the MPP. So no additional evaluation of the probabilistic constraint is required in the deterministic optimization in SORA. The proposed RBDO method is applied to numerical examples and compared to various RBDO methods. It is shown that the proposed method is very efficient with similar accuracy.     

Reliability-based design optimization with discrete design variables and non-smooth performance functions: AB-PSO algorithm

The purpose of reliability-based design optimization (RBDO) is to find a balanced design that is not only economical but also reliable in the presence of uncertainty. Practical applications of RBDO involve discrete design variables, which are selected from commercially available lists, and non-smooth (non-differentiable) performance functions. In these cases, the problem becomes an NP-complete combinatorial optimization problem, which is intractable for discrete optimization methods. Moreover, the non-smooth performance functions would hinder the use of gradient-based optimizers as gradient information is of questionable accuracy. A framework is presented in this paper whereby subset simulation is integrated with a new particle swarm optimization (PSO) algorithm to solve the discrete and non-smooth RBDO problem. Subset simulation overcomes the inefficiency of direct Monte Carlo simulation (MCS) in estimating small failure probabilities, while being robust against the presence of non-smooth performance functions. The proposed PSO algorithm extends standard PSO to include two new features: auto-tuning and boundary-approaching. The former feature allows the proposed algorithm to automatically fine tune its control parameters without tedious trial-and-error procedures. The latter feature substantially increases the computational efficiency by encouraging movement toward the boundary of the safe region. The proposed auto-tuning boundary-approaching PSO algorithm (AB-PSO) is used to find the optimal design of a ten-bar truss, whose component sizes are selected from commercial standards, while reliability constraints are imposed by the current design code. In multiple trials, the AB-PSO algorithm is able to deliver competitive solutions with consistency. The superiority of the AB-PSO algorithm over standard PSO and GA (genetic algorithm) is statistically supported by non-parametric Mann-Whitney U tests with the p-value less than 0.01.     

An approach to reliability-based optimization of redundant structures

This paper proposes an optimum design procedure for redundant structures with the constraints on the formation probabilities of structural failure modes. Although there exist numerous failure modes in a large-scale redundant structure, it is found that only a representative group consisting of some dominant failure modes needs to be considered in the optimization process. The proposed procedure introduces such dominant modes step by step from various design stages to keep the total number of the constraints at a minimum level. A branch-and-bound technique is used to identify dominant failure modes in a design state. Some analytical methods are discussed for the calculation of the formation probabilities of failure modes in the optimum design process. A numerical example is given to illustrate the effectiveness of the proposed procedure.     

Reliability-based design in rock engineering: Application of Bayesian regression methods to rock strength data

Reliability-based design(RBD) is being adopted by geotechnical design codes worldwide, and it is therefore necessary that rock engineering practice evolves to embrace RBD. This paper examines the Hoek-Brown(He B) strength criterion within the RBD framework, and presents three distinct analyses using a Bayesian approach. Firstly, a compilation of intact compressive strength test data for six rock types is used to examine uncertainty and variability in the estimated He B parameters m and sc, and corresponding predicted axial strength. The results suggest that within-and between-rock type variabilities are so large that these parameters need to be determined from rock testing campaigns, rather than reference values being used. The second analysis uses an extensive set of compressive and tensile(both direct and indirect) strength data for a granodiorite, together with a new Bayesian regression model, to develop joint probability distributions of m and scsuitable for use in RBD. This analysis also shows how compressive and indirect tensile strength data may be robustly used to fit an He B criterion.The third analysis uses the granodiorite data to investigate the important matter of developing characteristic strength criteria. Using definitions from Eurocode 7, a formal Bayesian interpretation of characteristic strength is proposed and used to analyse strength data to generate a characteristic criterion.These criteria are presented in terms of characteristic parameters mkand s ck, the values of which are shown to depend on the testing regime used to obtain the strength data. The paper confirms that careful use of appropriate Bayesian statistical analysis allows the He B criterion to be brought within the framework of RBD. It also reveals that testing guidelines such as the International Society for Rock Mechanics and Rock Engineering(ISRM) suggested methods will require modification in order to support RBD. Importantly, the need to fully understand the implications of uncertainty in nonlinear strength criteria is identified.     

浅谈某高层住宅楼结构设计优化

钢筋混凝土剪力墙高层住宅已成为城市主要建筑结构类型。本文阐述了高层住宅楼结构优化设计的方法和途径,并结合工程实例,进行具体的说明论证。结构设计的优化不是以牺牲建筑结构安全度和抗震性能来求得经济效益的。结构的优化不仅在结构本身,而且涵盖建筑的其他方面,如选择合适的建筑方案,提高建筑空间效率和改善建筑的性价比等。     

Reliability-based design of ground improvement for liquefaction mitigation

The main purpose of this research is to develop a calculation method to assess the probability of liquefaction and a reliability-based design method to mitigate the liquefaction in sandy grounds. The probability of liquefaction is evaluated with the proposed model by considering the spatial variability of the soil parameters and the statistical characteristics related to the occurrence of earthquakes. The liquefaction resistance is calculated from the SPT N-value, the median grain size, D₅₀, and the fines content, F_c, through the empirical relationship [Iwasaki T, Arakawa A, Tokida, K. Simplified procedure for assessing soil liquefaction during earthquakes. Proc Soil Dyn Earthquake Eng Conf 1982;925–39]. The statistical models for these three soil parameters are determined with the maximum likelihood method. The occurrences of earthquakes is modeled based on the maximum annual acceleration found in historical earthquake data records. In this study, the probability of liquefaction is evaluated multi-dimensionally using the cokriging method. Finally, the reliability-based design method is discussed in order to determine the optimum design for ground improvement using sand compaction piles (SCP) based on the calculated probability of liquefaction.     

Reliability-based optimization of laterally loaded piles

A general approach to the reliability-based analyses and the optimum designs of laterally loaded piles (LLOP) is presented. This approach takes into consideration all behavior and side constraints specified by standard specifications for piles. Additionally, the casual effect of corrosion of piles with time is considered in formulation with limiting state functions. The solution to reliability-based problems is obtained by a computer program (RELLOP). A general reliability based methodology is developed and implemented in the developed computer program (RELLOP) for both element and system limit states. Numerical examples demonstrating the feasibility of considering multiple limit states and system reliability requirements in the design of laterally loaded piles are presented. Effects on the reliability-based design solution of allowable reliability levels, and time of exposure to corrosion are also illustrated.     

Transforming reliability limit-state constraints into deterministic limit-state constraints

This research proposes an efficient methodology that can transform a reliability limit-state constraint into a deterministic limit-state constraint. This new method may have broad applications in reliability-based design and optimization. The method is based on subset simulation and is applicable to general systems, e.g. linear or nonlinear systems and static and dynamical systems with high-dimensional uncertainties. Once the reliability constraint is transformed into a deterministic one, it is no longer necessary to conduct reliability analyses to verify the former. This can potentially save lots of computational time during the process of reliability-based design and optimization. The main idea of the new method is the introduction of the limit-state factor and nominal limit-state function, from which a deterministic nominal limit-state constraint is established. We propose two methods of establishing this nominal constraint, and they are verified with several simulated examples, showing that the established nominal constraint is indeed a satisfactory approximation of the target reliability constraint. Finally, we propose a simplified procedure requiring only two reliability analyses that can effectively transform reliability constraints into deterministic nominal constraints.     

结构形态创构方法——改进进化论方法及其工程应用

在建筑方案设计中,采用结构计算的方法来帮助建筑师确定建筑的形态具有工程意义。模仿自然界的进化现象,本文提出了一种结构形态的创构方法。该方法利用有限元法,计算结构相关力学特性(如von Mises应力分布),通过进行等值线(面)分析来评价结构承受荷载的效率,利用对曲线(面)进行“保留、淘汰、补充”的操作使结构体逐步进化并演变成合理结构。文中对该方法在两个实际工程设计中的应用进行了详细分析,并从提高进化效率的角度讨论了初始形状的合理选择。该方法可以对不同设计变量(比如约束条件,空间条件)进行设定从而得出不同建筑形态,给设计人员提供多种可参考的合理方案。利用此方法所得到的结构形态通常可以抑制弯矩产生,保证应力分布均匀且以轴力效应为主。最后讨论了该方法的有效性和实用性。     

Reliability-based optimization of structural systems by adaptive target safety – Application to RC frames

Reliability-based design optimization (RBDO) aims to find the best compromise between cost reduction and safety assurance. Traditionally, component optimization is defined by minimizing the structural cost under a prescribed reliability target for a single limit state. However, as structural failure is rarely devoted to only one component, the system approach becomes necessary to deal with realistic applications. In this paper, a methodology for system reliability-based design optimization (SRBDO) is proposed. Instead of specifying identical predefined component targets, the method is based on adaptive target reliabilities for structural components. An updating procedure is included in the optimization process to ensure the required system reliability. The proposed method aims to find the best compromise between satisfying the target system reliability and optimizing the component performance. The application to reinforced concrete structures shows the interest of the adaptive target reliabilities as well as the efficiency of the updating procedure.     

Reliability-based load factors for airblast and structural reliability of reinforced concrete columns for protective structures

Reliability-based design allows the decision-maker to select the level of reliability for a specific explosive blast loading scenario. Important to this is an understanding of airblast and resistance uncertainty. Reliability-based load factors are calculated and are dependent on the variability of model error, explosive mass and range. Reliability-based design load factors (RBDFs) are estimated for explosive ordnance, terrorism, weaponeering and other scenarios. The effect of RBDFs on structural reliabilities for reinforced concrete (RC) columns is then calculated where resistance and loading are random variables, and compared to target values. It was found, for realistic combinations of range and explosive mass variabilities, that RC columns designed to existing standards have a significant margin of safety with a probability of failure of 1?×?10^?3 to 1?×?10^?5. However, if there is large airblast variability, then the application of RBDFs is necessary to ensure that safety levels are acceptable according to international standards.     

Reliability-based integrated design of steel portal frames with tapered members

Integrated structural designs, with consideration of system reliability for steel portal frames comprising tapered members, are studied in this paper. The reliability-based integrated design (RID) directly checks the structural system limit states and the corresponding system reliability, based on structural nonlinear analysis. The nonlinear integrated analysis model, the semi-analytical simulation method employed for system reliability assessment, the development processes of RID format and the design application of RID formula and curves are presented in this paper. Design examples and comparisons among three different design formats demonstrate that RID proposed in this paper is of certain and consistent system reliability levels, and provides a feasible way for structural engineers to improve the design quality and flexibility of steel frame structures.     

改进的双向渐进结构拓扑优化方法

对渐进结构优化方法进行了介绍,阐述了双向渐进结构拓扑优化步骤,针对拓扑优化中的常见问题提出了相应的改进措施,给出了拓扑优化的性能评价指标,并结合工程实例验证了改进后方法的有效性,以得到满意的拓扑结果。     

A framework for reliability-based system assessment based on structural health monitoring

The safety and usability of transport infrastructures is of great importance for the entire society, because disturbances of traffic networks can have significant consequences for the economy and the environment. Especially today, when bad news about deteriorated structures and shortened public budgets are omnipresent, this must not be forgotten. Structural health monitoring (SHM) can help to ensure the safety of deteriorated structures. SHM is expensive and therefore the investigation of optimized inspection and monitoring strategies is an active field of research. The Collaborative Research Centre (CRC) 477 at the Braunschweig University of Technology investigates innovative methods for SHM. In project field A1, a framework for the probabilistic safety assessment of structures has been developed using data from SHM. The current paper describes and explains the methodology of the framework and shows its application using a substitute structure, which was built for the CRC 477.     

Structural optimization for performance-based design in earthquake engineering: Applications of neural networks

This work addresses an approach to performance-based design in the context of earthquake engineering. The objective is the optimization of the total structural cost, under constraints related to minimum target reliabilities specified for the different limit states or performance requirements. The problem involves (1) the use of a nonlinear, time-stepping dynamic analysis to investigate the responses of relevance to the performances’ evaluation and (2) the integration of the responses into measures of damage accumulated during the earthquake. The random responses are deterministically obtained for different combinations of the design parameters and the intervening random variables, of which some are associated with the structure and some with the earthquake characteristics. The approach uses a neural network representation of the responses and, for each one, the variability associated with different earthquake records is accommodated by developing two networks: one for the mean response over the records, and another for the corresponding standard deviation. The neural network representation facilitates the estimation of reliability by Monte Carlo simulation, and the reliability achieved in each performance level, for a specific combination of the design parameters, is itself represented with a neural network. This is then used within an optimization algorithm for minimum total cost under reliability constraints. An application example uses a reinforced concrete, multi-storey plane structure with seismic demands corresponding to the city of Mendoza, Argentina.     

陆海空大厦结构优化设计

上海陆海空大厦在停建数年后,业主委托江欢成事务所对结构进行优化设计。原设计沿用常规做法,大体上能满足规范要求,但不够理想,例如柱子截面较大,自振周期较长,地震作用时层间位移角也较大,补桩太多等等。本优化设计不但取得了十分明显的经济效益,而且大大改善了室内空间环境。东西塔楼共44根柱子,拔掉了16根,柱子断面进一步减小,核心筒内部剪力墙厚度进一步减小,楼盖厚度进一步减小,节约混凝土8400m3,增加使用面积约1300m2。取消了主楼和裙房之间的沉降缝,减少补桩208根。综合经济效益约2000万元人民币。     

Bioinspired architectural design based on structural topology optimization

This paper aims to present a new approach for using structural topology optimization to evaluate and generate bioinspired architectural design. To investigate these possibilities, we present several experiments in two and three-dimensional domains under a variety of load and support conditions that are inspired by nature. These experiments are based on structural topology optimization techniques, which have shown to be viable for fostering innovative ideas to solve complex building stability problems. Moreover, these techniques enable fruitful collaborations between architects and engineers in the early stages of the design process. We compare the optimal solutions with different species of plants and animals and evaluate their potential use as a structural system through visual and quantitative analyses. Results reinforce the efficacy of using topology optimization in the development of bioinspired structures and, as such, its future use in creative design contexts.     

Investigation of the structural form optimization methods of high-rise buildings

In this paper, the structural form optimization methods of high-rise buildings based on the expert system (ES), case-based reasoning (CBR), and knowledge discovery in database (KDD) are evaluated systematically. The characteristics and shortcomings of each method are pointed out. It is predicted that the incorporation of these three techniques into an intelligent form optimization method will be an important development direction in the future. Finally, the unified intelligent form selection model combined with concepts of ES, CBR, KDD and artificially intelligent beautification is proposed. In consideration of the needs of human beings, machinery and computation, the model has been used for structural design combined with relevant knowledge, means, maneuver and strategy. The model plays an important role and has practical value in the process of artificially intelligent form optimization. It effectively reduces the blindness and failure of computer-aided structural design. Translated from Journal of Harbin Institute of Technology, 2006, 38(2): 195–198, 319 [译自: 哈尔滨工业大学学报]     

Genetic evolutionary structural optimization

Evolutionary structural optimization (ESO) is based on a simple idea that an optimal structure (with maximum stiffness but minimum weight) can be achieved by gradually removing ineffectively used materials from design domain. In general, the results from ESO are likely to be local optimums other than the global optimum desired. In this paper, the genetic algorithm (GA) is integrated with ESO to form a new algorithm called Genetic Evolutionary Structural Optimization (GESO), which takes the advantage of the excellent behavior of the GA in searching for global optimums. For the developed GESO method, each element in finite element analysis is an individual and has its own fitness value according to the magnitude of its sensitivity number. Then, all elements in an initial domain constitute a whole population in GA. After a number of generations, undeleted elements will converge to the optimal result that will be more likely to be a global optimum than that of ESO. To avoid missing the optimum layout of a structure in the evolution, an interim thickness is introduced into GESO and its validity is demonstrated by an example. A stiffness optimization with weight constraints and a weight optimization with displacement constraints are studied as numerical examples to investigate the effectiveness of GESO by comparison with the performance of ESO. It is shown through the examples that the developed GESO method has powerful capacity in searching for global optimal results and requires less computational effort than ESO and other existing methods.     

Reliability-based design of medium mast lighting structural supports

Rural intersections and interchanges often require lighting for driver safety. Although high mast lighting supports, sometimes as tall as 50 m have been installed in many locations, it is becoming apparent that light pollution to nearby residences is an issue. As a response to this problem, the Colorado Department of Transportation is moving towards the use of medium mast lights which are typically 15–20 m in height. This article presents the results of a numerical investigation to develop reliability-based design charts as a function of several key design variables and the mean wind velocity at a site. These medium-mast structures are less than 1 m in diameter at the base and are quite flexible relative to many civil engineering structures. The limit state function is formulated in terms of fatigue life and is computed based on the moments at the base that are produced during multi-mode dynamic excitation as a result of the wind loading. Morison's equation, which provides relative force for slender bodies as a function of flow velocity, was applied within a dynamic finite element framework in order to account for the relative motion between the wind and the motion of the structure. Then, a well-known random vibrations approach was coupled with Miner's rule to estimate the fatigue life of the structural support. Reliability-based design charts for several different design variables such as wall thickness and outside diameter are presented.